Phone numbers consist of a three-digit area code followed by seven digits. If the area code must have a 0 or1 for the second digit, and neither the area code nor the seven-digit number can start with 0 or 1, how many different phone numbers are possible? How did you come up with your answer?
a.
8 times 10 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 = 6,400,000,000
b.
8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 = 1,280,000,000
c.
8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 = 128,000,000
d.
8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 times 10 = 12,800,000,000



Please select the best answer from the choices provided

Answer: $4.16

Step-by-step explanation:

20% of 63.20 = 12.64
63.20 + 12.64 = 75.84

80.00 - 75.84 = 4.16

Answer:

it is 19 brainliest please

Step-by-step explanation:

Answer: yes he can transport them all

Step-by-step explanation: yes.

Answer:

585.14

Step-by-step explanation:

3677=2πr

r=3677÷44/7

=585.14

The calculated height of the​ lighthouse, h will be yards

From the question, we have the following parameters that can be used in our computation:

Similar triangles of shadows and house

This means that

Ratio = Division or ratio of corresponding sides

So, we have

h : 9 = 18 : 6

So, we have the following representation

h/9 = 18/6

This gives

h = 9 * 18/6

By calculation, we have

height = 27 yards

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An r value of 0 in a correlation analysis indicates that there is no linear relationship between the two quantities being analyzed.

This means that there is no correlation between the two variables, and any observed pattern or association between them is likely due to chance. In other words, the values of one variable do not predict the values of the other variable. However, it is important to note that a correlation analysis only measures linear relationships, and there may still be other types of relationships between the variables that are not captured by the r value.

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Answer:

  an = 1/2n² -1/2n -2

Step-by-step explanation:

You want a formula for the n-th term of the quadratic sequence -2, -1, 1, 4.

Using x = 1, 2, 3 and y = -2, -1, 1 we can write equations for the coefficients a, b, c of the quadratic expression ax² +bx +c.

  a(1²) +b(1) +c = -2

  a(2²) +b(2) +c = -1

  a(3²) +b(3) +c = 1

Subtracting the first equation from the other two, we get ...

  3a +b = 1

  8a +2b = 3

Subtracting twice the first from the second of these, we get ...

  (8a +2b) -2(3a +b) = (3) -2(1)

  2a = 1

  a = 1/2

Then b can be found from ...

  b = 1 -3a = 1 - 3/2 = -1/2

And c can be found from ...

  -2 -b -a = c = -2 -(-1/2) -(1/2) = -2

The formula is ...

  an = 1/2n² -1/2n -2

__

Additional comment

For systems of equations, the solver used in the second attachment works well. It tells us (a, b, c) = (1/2, -1/2, -2) as we found above.

Alternate solution

The first differences of the given terms are ...

  1, 2, 3

And their differences are ...

  1, 1

The coefficient of n² is half this second-difference value: 1/2.

If you subtract 1/2n² from the given terms, you get ...

  -5/2, -3, -7/2, -4

This arithmetic sequence has the formula ...

  a1 +d(n -1)

  -5/2 +(-1/2)(n -1) = -1/2n -2

Adding this to the term we subtracted gives ...

  an = 1/2n² -1/2n -2 . . . . . as above

The maximum weight of clothes that can be shipped in the box without exceeding the weight limit for shipping is 47 pounds.

To determine the maximum weight of clothes that can be shipped in the box, we first need to know the weight limit for shipping. This will vary depending on the shipping method and destination. Let's assume that the weight limit for shipping is 50 pounds.

We subtract the weight of the empty box from the weight limit for shipping: 50 pounds - 3 pounds = 47 pounds.

It is always a good idea to check the specific weight limit for the shipping method and destination before packing and shipping any items to avoid any issues or additional fees.

The complete question is:

What is the maximum weight of clothes that can be shipped in the box without exceeding the weight limit for shipping?

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Answer: 23

Step-by-step explanation:

     The range of the data set is the same thing as subtracting the smallest value from the largest value.

     Here, our smallest value is 8 and our largest value is 31.

                 31 - 8 = 23

     This data set has a range of 23.

4,516,932,420 committees can be formed if each committee must have 4 republicans and 3 democrats

We have,

Republicans= 55

Democrats = 44

Independent= 1

Using Combination, the number of committees can be formed

= C(55, 4) / C(44, 3)

= 55! / 4! (55-4)! ÷ 44!/ 3! (44-3)!

= 55! / 4! 51! x 44! / 3! 41!

= 55 x 54 x 53 x 52 x 44 x 43 x 42/ 4 x 3 x 2 x 3 x 2

= 650,438,268,480 / 144

= 4,516,932,420

Thus, there are 4,516,932,420 committees can be formed.

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Answer:

y = -5x + 4.

Step-by-step explanation:

Slope-intercept formula: y = mx (m is slope) + B (y-intercept)

Plug in it:

y = 5x + 4.

Answer:

Step-by-step explanation:

Part A:

Let's use the information given in the problem to create the inequalities:

Each batch of chicken soup takes 3 hours to prepare, so the total preparation time for c batches of chicken soup is 3c hours.

Each batch of beef barley takes 3.5 hours to prepare, so the total preparation time for b batches of beef barley soup is 3.5b hours.

Each batch of chicken soup takes 4 hours to package, so the total packaging time for c batches of chicken soup is 4c hours.

Each batch of beef barley takes 2 hours to package, so the total packaging time for b batches of beef barley soup is 2b hours.

There are 5 preparation workers who work 40 hours per week, so the total preparation time available is 5 workers x 40 hours/worker = 200 hours.

There are 6 packaging workers who work 40 hours per week, so the total packaging time available is 6 workers x 40 hours/worker = 240 hours.

To create the system of inequalities, we need to make sure that the total preparation and packaging times for both types of soup do not exceed the available time. Therefore:

3c + 3.5b ≤ 200 (total preparation time ≤ available preparation time)

4c + 2b ≤ 240 (total packaging time ≤ available packaging time)

Also, we have the non-negativity constraints:

c ≥ 0 (number of batches of chicken soup is non-negative)

b ≥ 0 (number of batches of beef barley soup is non-negative)

Therefore, the system of inequalities is:

3c + 3.5b ≤ 200

4c + 2b ≤ 240

c ≥ 0

b ≥ 0

Part B:

To find two possible combinations of batches of chicken soup and beef barley soup that could be made in one week based on the constraints, we can try different values for c and b that satisfy the inequalities from Part A. Here are two possible combinations:

Combination 1: c = 40, b = 0

Total preparation time: 3c + 3.5b = 3(40) + 3.5(0) = 120

Total packaging time: 4c + 2b = 4(40) + 2(0) = 160

Both inequalities are satisfied, and c and b are non-negative.

Therefore, in one week, the company can make 40 batches of chicken soup and 0 batches of beef barley soup.

Combination 2: c = 30, b = 20

Total preparation time: 3c + 3.5b = 3(30) + 3.5(20) = 135

Total packaging time: 4c + 2b = 4(30) + 2(20) = 160

Both inequalities are satisfied, and c and b are non-negative.

Therefore, in one week, the company can make 30 batches of chicken soup and 20 batches of beef barley soup.

Answer:

3

Step-by-step explanation:

The discounted cost for an entire year of service with cell-to-cell would be = $450

The fixed rate for cell-to-cell services for a month = $50

Therefore the cost for a year would be = 50×12 = $600

The percentage of discount on the coupon = 25%of cost Price.

That is 25% of 600

= 25/100 × 600/1

= 25×6

= $150

Therefore, the discounted cost for an entire year of service with cell-to-cell would be = 600-150=$450

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Answer:49.4g

Step-by-step explanation:

After considering the given data we conclude that the total amount of trace element collected by Abdoulaye is 4 grams.

Formula for volume of a cylinder
[tex]V = \pi r^2 h[/tex]
Here,
Radius = 13.4 / 2 = 6.7 cm
Height = 10.3
Then
V = 3.14 × (6.7)² × 10.3
V = 1,451.8 cubic centimeters
Volume of cylinder is approximately 1,451.8 cubic centimeters.

In the event a water sample shows  0.034 grams  of some trace element for every cubic centimeter of water, then the amount of trace element in the sample can be evaluated by multiplying the volume of the sample by the concentration of the trace element in the water sample.
1.451.8 × 0.034 = 49.36 grams
Then , approximately 49.36 grams of trace element has Abdoulaye collected rounding the value to the nearest tenth which is 4 grams.

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Answer:

5.6 miles

Second answer option

Step-by-step explanation:

From the tables we see that 1 mile ≈ 1.61 km

Therefore 1 km ≈ 1/1.61 mile

9 km ≈ 9 x 1/1.61 ≈ 9/1.61 ≈ 5.592341 miles

Rounded to first decimal(tenth) that would be 5.6 miles

This is the second answer option

Option a. The graph that would correctly display the data that we have jere would be: a bar graph titled favorite topping with the x-axis labeled topping and the y-axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27, and the fourth bar labeled chocolate chips going to a value of 44.

The correct graph to display this type of categorical data is a bar graph. The correct option should show the data with the correct number of customers for each topping as it is listed in the question we have :

Sprinkles: 17

Nuts: 12

Hot Fudge: 27

Chocolate Chips: 44

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When, a 30 gram sample of a substance that's used to sterilize surgical instruments has a k value of 0.1253. Then, the half-life of the substance is 8.0 days.

The half-life of a substance is the amount of time it takes for half of the initial amount of the substance to decay. The decay of the substance can be modeled using the formula;

N = N0 × [tex]2^{(-kt)}[/tex]

where N is the amount of substance at time t, N0 is the initial amount of substance, k is the decay constant, and t is the time.

In this case, we know that the initial amount of the substance is 30 grams, and the decay constant (k value) is 0.1253. We want to find the half-life, which we can denote as [tex]t_{1/2}[/tex]

When half of the initial amount of substance remains, the amount of substance is [tex]N_{0}[/tex]/2. So we can substitute N = [tex]N_{0}[/tex]/2 and solve for [tex]t_{1/2}[/tex];

N = [tex]N_{0}[/tex]/2

[tex]N_{0}[/tex]/2 = [tex]N_{0}[/tex] × [tex]2^{(-kt1/2)}[/tex]

1/2 = [tex]2^{(-kt1/2)}[/tex]

log2(1/2) = log2([tex]2^{(-kt1/2)}[/tex])

-1 = [tex]-kt_{1/2}[/tex]

[tex]t_{1/2}[/tex] = 1/k × log2(2)

[tex]t_{1/2}[/tex] = 1/k

Substituting the given value of k, we get:

[tex]t_{1/2}[/tex] = 1/0.1253

[tex]t_{1/2}[/tex] ≈ 7.9816

Therefore, the half-life of the substance is approximately 8.0 days.

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The probability that a 6 is obtained on at least one of the rolls is 67%.

The probability of getting a 6 on one roll of a fair die is 1/6. The probability of not getting a 6 on one roll is 5/6.

Let's use the complementary probability approach to calculate the probability of getting no 6 on any of the 5 rolls. The probability of not getting a 6 on one roll is 5/6, so the probability of not getting a 6 on all 5 rolls is (5/6)^5 ≈ 0.327.

Therefore, the probability of getting at least one 6 on 5 rolls is 1 - 0.327 ≈ 0.673.

So the probability of getting at least one 6 on 5 rolls of a fair die is approximately 0.673, or 67.3% when rounded to three decimal places. This means that if you roll a fair die 5 times, you have about a 67% chance of getting at least one 6.

Correct Question :

A fair die is rolled 5 times. What is the probability that a 6 is obtained on at least one of the rolls? Round your answer to three decimal places.

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The statistical measures are: Min: 6 Q1: 7 Med: 11.5 Q3: 13 Max: 15.

The box and whiskers plot is given below.

To create a box and whiskers plot, we have to first derive the statistical measures of the data set given, which is the five number summary that include, the mina nd max values, the median, and the quartiles.

Given the data set, 6, 7, 7, 8, 10, 13, 13, 13, 15, 15, the five number summary which are the statistical measures are:

Minimum: 6 (lowest value)

First Quartile: 7 (middle of the first half of the data)

Median: 11.5 (center of the data set)

Third Quartile: 13 (middle of the second half of the data)

Maximum: 15 (largest value).

The box and whiskers plot of the data set, 6, 7, 7, 8, 10, 13, 13, 13, 15, 15, is shown in the diagram attached below.

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The measure of m∠2 is given as 130

Since ∠1 and ∠4 are supplementary, their sum equals 180°:

m∠4 = 180° - m∠1

m∠4 = 180° - 50°

m∠4 = 130°

Now, we need to find m∠2. Since lines m and n cross, forming vertical angles, m∠1 is vertical to m∠3 and m∠2 is vertical to m∠4. Vertical angles are equal, so:

m∠2 = m∠4

m∠2 = 130°

Thus, m∠2 is 130°.

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Therefore, when x is 13, y is 52 if y varies directly with x.

In mathematics, an equation is a statement that two expressions are equal. It is usually written using an equal sign (=). Equations can contain variables, which are usually represented by letters, and the goal is often to solve the equation for the value(s) of the variable(s) that make the equation true.

Here,

If y varies directly with x, then we can write the relationship between y and x using the equation:

y = kx

where k is the constant of proportionality. To solve for k, we can use the given information that when x is 7, y is 28:

28 = k(7)

Solving for k, we get:

k = 4

Now that we know k, we can use the equation to find y when x is 13:

y = 4(13)

y = 52

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Answer: 84 square inches.

Step-by-step explanation:

Side A of shaded: 5+3+3 = 11

Side B of shaded: 3+3+3= 9

11x9= 99

99-(3x5{normal rectangle area})= 84

Expanded form of 804082 is 8 x 100000 + 0 x 10000 + 4 x 1000 + 0 x 100 + 8 x 10 + 2 x 1.

To write the number 804082 in expanded form, we need to break it down into its component parts based on place value.

Expanded form 1:

804082 = 8 x 100000 + 0 x 10000 + 4 x 1000 + 0 x 100 + 8 x 10 + 2 x 1

In this expanded form, we can see that the digit 8 is in the hundred thousands place, the digit 0 is in the ten thousands place, the digit 4 is in the thousands place, the digit 0 is in the hundreds place, the digit 8 is in the tens place, and the digit 2 is in the ones place.

Expanded form 2:

804082 = 8 x [tex]10^{5}[/tex] + 0 x [tex]10^{4}[/tex] + 4 x [tex]10^{3}[/tex] + 0 x [tex]10^{2}[/tex] + 8 x [tex]10^{1}[/tex] + 2 x [tex]10^{0}[/tex]

In this expanded form, we can see that each digit in the number is multiplied by its corresponding power of 10 based on its position in the number.

Both forms give us the same result, but they express the number in different ways based on the place value of each digit.

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When excluding stoppages, the speed of a bus is 54 km/h, and including stoppages, it is 36 km/h. the bus stop is 20 minutes per hour

We have to Calculate the distance traveled by bus in 1 hour excluding stoppages and calculate the distance traveled by bus in 1 hour including stoppages. Then we have to calculate the time taken to cover that difference between the distances and convert the calculated time into minutes.

Given data:

The speed of a bus while excluding stoppages = 54 km/h.

the speed of the bus while including stoppages = 36 km/hr.

From the given data we can say that:

The Distance traveled by bus in 1 hour, excluding stoppages is = 54 km.

The Distance traveled by bus in 1 hour, including stoppages, is = 36 km.

Distance traveled = Distance traveled by bus in 1 hour excluding stoppages – distance traveled by bus in 1 hour including stoppages

= 54km − 36km = 18km

The bus covers 18 km less due to stoppages.

the time taken to cover18 km, = distance traveled / speed of the bus

= 18km / 54km/hour

= 1 / 3 hour

Time taken in minutes = ( 1 / 3×60 )minutes

=20minutes

Therefore, the bus stops per hour for 20 minutes.

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If we repeated this procedure many times, the average number of points scored by our sample of 30 students will be between 344 and 406 points approximately 90% of the time.

This means that we are 90% confident that the true population mean of points scored by all students at the high school falls within this range based on the sample of 30 students who played the game for an hour.
A random sample of 30 students at a high school was allowed to play a popular cell phone game for an hour, yielding an average score of 375 with a standard deviation of 100. The 90% confidence interval is 375 ± 31. The statement that best summarizes the meaning of this confidence interval is: If we repeated this procedure many times, the average number of points scored by our sample of 30 students will be between 344 and 406 points approximately 90% of the time.

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Answer:

The answer to your problem is, 12 1/2

Step-by-step explanation:

As shown to the problem we would need to add

4 1/2 + 2 7/12

Lets make them equivalent denominators:

1/2 & 7/12

= 24

1/2 = 12/24

7/12 = 14/24

Then make the new problem into;

4 12/24 + 7 14/24

= 12 1/2

Thus the answer to your problem is, 12 1/2

Answer:

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where:

A = the balance after t years

P = the principal amount (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this problem, P = $6,500, r = 0.084, n = 12 (monthly compounding), and t = 12. Plugging in these values, we get:

A = $6,500(1 + 0.084/12)^(12*12)

A = $6,500(1.007)^144

A = $6,500(2.008)

A = $13,052.20

Therefore, the balance after 12 years is $13,052.20 when the interest is compounded monthly.

The percentage of values and the z-scores are listed below

Here, we have

Between z = 0.53 and 2.67

This is represented as

Percentage = (0.53 < z < 2.67)

Using a graphing calculator, we have

Percentage = 29.43%

Next, we have

To the right of z = 1.61

This is represented as

Percentage = x > 1.61

Using a graphing calculator, we have

Percentage = 5.40%

Here, we have

Percentage = 35% to the left of the z-score

This means that

P(z < z) = 0.35

Using a graphing calculator, we have

z =  -0.385

Next, we have

Percentage = 18% to the right of the z-score

This means that

P(z > z) = 0.18

Using a graphing calculator, we have

z =  0.915

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